Papers by Keyword: Algebra

Abstract: This paper aims to prove the existence of the solutions of some operator functional equations of sinus type in universally bounded operator algebra, where the operator is defined on a locally convex space. Some results based on the work of B. Sz.-Nagy following the representation model of operator groups are established.

Abstract: The popular fuzzy c-means algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. However, Gustafson-Kessel clustering algorithm needs added constraint of fuzzy covariance matrix, Gath-Geva clustering algorithm can only be used for the data with multivariate Gaussian distribution. In GK-algorithm, modified Mahalanobis distance with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. In this paper, an improved Normalized Supervised Clustering Algorithm Based on FCM by taking a new threshold value and a new convergent process is proposed. The experimental results of real data sets show that our proposed new algorithm has the best performance. Not only replacing the common covariance matrix with the correlation matrix in the objective function in the Normalized Supervised Clustering Algorithm.